The present invention relates to a method for 3D modelling of the impedance of a heterogeneous medium from waves reflected by the discontinuities of the medium, in response to waves emitted in the medium. The waves used can be elastic waves emitted by a seismic source etc.
Various well-known approaches for converting seismic data into acoustic impedances differ in the method of parameterization of the impedance model, in the definition of objective functions and in the possibility of introducing a priori information. Parameterization can be concise, the impedance being constant or linear in a vertical direction in a certain number of layers of unknown geometry. The unknown parameters are here the acoustic impedances as well as the locations and the number of interfaces.
A method for modelling a physical parameter such as the acoustic impedance of a heterogeneous medium is described for example in the assignee""s patent EP-0,354,112.
Parameterization can also be denser, the impedance field being discretized by using a 3D grid pattern. The seismic objective function consists of a norm of a well-known type L1 for example or L2 of the difference between the synthetic data and the observed data. The synthetic data result from the convolution of a given optimum wavelet, calibrated at the well locations with the series of reflection coefficients calculated from the impedance log. The quantity concerned in the geological objective function can be the impedance itself or some of the derivatives thereof, especially in the direction of the layers. The types of constraints applied to these quantities can be a norm of type L1 or the square of a norm L2 of the difference between the optimum model and the a priori model, and of the equalities or inequalities between the quantity sought and known numerical values. The most commonly used optimization methods are the conjugate gradient methods or techniques referred to as xe2x80x9csimulated annealingxe2x80x9d techniques.
It is well-known from Brac J. et al: xe2x80x9cInversion with A Priori Information: an Approach to Integrated Stratigraphic Interpretationxe2x80x9d, in Sheriff R. E. Ed., Reservoir Geophysics, Soc. Expl. Geophys., Investigations in Geophysics 7, to choose as the geological objective function the square of the norm L2 of the impedance difference and of the impedance gradient difference, after projection onto the direction of dip in the vertical plane of the seismic lines. Inversion of a 3D block thus consists in several multitrace 2D inversions applied seismic line after seismic line, even if the a priori model is three-dimensional.
The reliability and the accuracy of reservoir models depend on the degree of integration between the seismic and the geologic data. A realistic reservoir model must combine, at the earliest possible stage of the implementation process, relatively accurate poststack seismic data, laterally few but vertically accurate well logging data, as well as interpretative data provided by a regional geological survey. Poststack stratigraphic inversion is a significant step for the integration of geosciences.
In the description hereafter, the general term xe2x80x9cfoliatedxe2x80x9d volume or volume provided with a xe2x80x9cfoliationxe2x80x9d, used to define the medium to be modelled, is taken in its geometrical meaning. It is a volume consisting of a set of contiguous and disjointed sheets or surfaces whose gathering forms the volume.
The method according to the invention finds applications notably for subsoil surveys for example in hydrocarbon reservoir prospecting.
The of the method according to the invention determines a three-dimensional (3D) optimum model of the impedance of a heterogeneous medium from recorded data corresponding to waves coming from the heterogeneous medium, in response to waves that are transmitted therein and from a 3D a priori model of this heterogeneous medium, knowing the position of different impedance discontinuities of the medium, and after stratigraphic interpretation.
The method is characterized, in the most general definition thereof, in that it comprises in combination
constructing a 3D geometric model of the heterogeneous medium, comprising several foliated volumes (provided with a foliation) with definition (positioning) of the various sheets thereof,
constructing an a priori impedance model from this geometric model and from a plurality of impedance measurements taken at various depths of the heterogeneous medium,
selecting a covariance model alone the sheets of said foliations, and
forming the optimum model by recorded data inversion using the a priori impedance model.
The method can be used notably to obtain a 3D optimum model of the impedance of a subsoil zone, the various foliated volumes being in this case sedimentary units, the impedance measurements being obtained at various depths of at least one well through the zone, and the sheets of the various foliated volumes consisting of deposition isochrones in each of these sedimentary units.
The a priori impedance model can be formed for example by simple interpolation or by kriging, along deposition isochrones, of the impedance values known for the well(s).
The recorded data can be obtained for example from elastic waves (P or S waves) or electromagnetic waves.
According to a preferred embodiment, an isotropic or anisotropic 2D exponential covariance model is preferably selected.
Formation of the optimum model can be obtained for example by determining, on the entire 3D model, the minimum of a global objective function comprising a term relative to the recorded data, consisting of the square of the norm L2 of the difference between synthetic data and the recorded data, and an impedance term consisting on the one hand of the square of the norm L2 of the impedance difference and, on the other hand, of the square of the norm L2 of the impedance difference gradient, after projection of this gradient onto the plane tangent to a local sheet of the foliated volumes (a dip plane in the case of a subsoil zone for example).
The method according to the invention is a flexible approach for estimating impedances in the frequency band used, constrained by the recorded 3D data, the impedance logs (measured in the wells for example) and the known information concerning the medium (geologic data, stratigraphic and structural as well for example).